5y^4+10y^3-40y^2=0

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Solution for 5y^4+10y^3-40y^2=0 equation:


Simplifying
5y4 + 10y3 + -40y2 = 0

Reorder the terms:
-40y2 + 10y3 + 5y4 = 0

Solving
-40y2 + 10y3 + 5y4 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '5y2'.
5y2(-8 + 2y + y2) = 0

Factor a trinomial.
5y2((-4 + -1y)(2 + -1y)) = 0

Ignore the factor 5.

Subproblem 1

Set the factor 'y2' equal to zero and attempt to solve: Simplifying y2 = 0 Solving y2 = 0 Move all terms containing y to the left, all other terms to the right. Simplifying y2 = 0 Take the square root of each side: y = {0}

Subproblem 2

Set the factor '(-4 + -1y)' equal to zero and attempt to solve: Simplifying -4 + -1y = 0 Solving -4 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1y = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1y = 0 + 4 -1y = 0 + 4 Combine like terms: 0 + 4 = 4 -1y = 4 Divide each side by '-1'. y = -4 Simplifying y = -4

Subproblem 3

Set the factor '(2 + -1y)' equal to zero and attempt to solve: Simplifying 2 + -1y = 0 Solving 2 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1y = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1y = 0 + -2 -1y = 0 + -2 Combine like terms: 0 + -2 = -2 -1y = -2 Divide each side by '-1'. y = 2 Simplifying y = 2

Solution

y = {0, -4, 2}

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